Mechanical performance of shotcrete shell accompanied with steel sets

[Display omitted] •Behaviour of shotcrete with steel sets in tunnels is modelled by analytical method;•The stiffness of hybrid support system is obtained in any locations along tunnel;•The non-uniform deformation of shotcrete between consecutive steel sets is obtained;•Developed bending moment on shotcrete between steel sets can be crucial for design;•A greater stiffness of steel set, a greater bending moment on shotcrete layer. The appropriate support system for tunnels in squeezing conditions is the hybrid supporting system consisting of steel sets and a shotcrete layer. The stiffness of this hybrid supporting system is variable between two consecutive steel sets, i.e., a greater value in the vicinity of the steel sets than in other locations. This is because, the contribution of steel sets to confine tunnel convergence is not uniform, but depends upon the distance to each steel frame. Accordingly, the tunnel convergence becomes non-uniform between two consecutive steel sets, and a bending moment is developed on the shotcrete layer, which may influence its design. In this paper, an analytical model is presented to simulate the shotcrete performance between two consecutive steel sets. For this purpose, the shotcrete layer is considered a shell fastened by consecutive steel rings. Using the principles of the theory of shells in the axisymmetric condition, it is assumed that the shotcrete is composed of longitudinal elements glued together from their sides. Therefore, the problem is simplified to analyzing continuous beams leaned on consecutive supports but subjected to loading from the radial and tangential directions. By employing the convergence confinement method, the non-uniform displacements are found. The results obtained with this theoretical simulation well agree with those of numerical modeling by FLAC3D. Therefore, the presented theoretical solution can provide a tool for the preliminary design of the shotcrete layer and an initial estimate of its performance to be used in more complicated numerical models. The results show that the non-uniform radial displacement and bending moment enhance by increasing the tunnel depth and decreasing the rock mass quality. As well, as the thickness of the shotcrete increases, the bending moment reduces.